Yes, consumers are also a stakeholder, but your typical consumer will receive very little or no direct benefit from this change. Eventually, yes, the profits will be reinvested, but the impact will be so diluted as to be a noticeable. Some small fraction of it will probably also go to tax evasion, being expatriated or sequestered by wealthy upper management.
Meanwhile, a whole lot of people are suddenly out of work, imposing significant negative externalities on them and their families. This could conceivably ruin a marriage, or turn a good parent into a raging alcoholic. It may well be that the negative gain to society (in the form of laying off so many employees) has severe follow-on effects, and in terms of net welfare this could do more harm than good.
The effects of leaving the workers out of the profit-sharing is more than just a matter of equity. Without redistribution of the welfare created by automation, it's perfectly conceivable that the net welfare gain is negative due to the negative second-order effects outweighing the positive second-order effects.
This is the stuff they don't teach you in Econ 101, but it's how things really work.